One reason for considering generalizations of the Kuramoto model (REF ) should come from a search for new phenomena not observed in the Kuramoto model. Thus, since Theorem REF  is true not only for the Kuramoto model but also for its Lie group generalizations in the form of (REF ), the merit of studying such models in the form of (REF ) will have to come from the behavior of the model when the particles are not extremely concentrated. For example, DeVille [1]} presents several special solutions to (REF ) and shows that it has multiple attractors under rich network topologies, while Ritchie, Lohe, and Williams [2]} present a detailed study of the global solutions of the special case \(G=SO(1,1)\) .
